Problem: Simplify the following expression: $p = \dfrac{z^2 - 13z + 36}{z - 4} $
Solution: First factor the polynomial in the numerator. $ z^2 - 13z + 36 = (z - 4)(z - 9) $ So we can rewrite the expression as: $p = \dfrac{(z - 4)(z - 9)}{z - 4} $ We can divide the numerator and denominator by $(z - 4)$ on condition that $z \neq 4$ Therefore $p = z - 9; z \neq 4$